Classification:
Biological Science
Systems Biology
Digital RNA Sequencing Minimizes Sequence-Dependent
Bias and Amplification Noise with Optimized Single
Molecule Barcodes
Katsuyuki Shiroguchi, Tony Z. Jia, Peter A. Sims, X. Sunney Xie*
Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford St., Cambridge,
Massachusetts 02138.
*Corresponding Author:
X. Sunney Xie
Department of Chemistry and Chemical Biology, Harvard University
12 Oxford St., Cambridge, Massachusetts 02138.
Tel:
617-496-9925
Email: xie@chemistry.harvard.edu
1
Abstract
RNA-Seq is a powerful tool for transcriptome profiling, but is hampered by sequence-dependent
bias and inaccuracy at low copy numbers intrinsic to exponential PCR amplification. We
developed a simple strategy for mitigating these complications, allowing truly digital RNA-Seq.
Following reverse transcription, a large set of barcode sequences is added in excess, and nearly
every cDNA molecule is uniquely labeled by random attachment of barcode sequences to both ends.
After PCR, we applied paired-end deep sequencing to read the two barcodes and cDNA sequences.
Rather than counting the number of reads, RNA abundance is measured based on the number of
unique barcode sequences observed for a given cDNA sequence. We optimized the barcodes to be
unambiguously identifiable even in the presence of multiple sequencing errors. This method
allows counting with single copy resolution despite sequence-dependent bias and PCR amplification
noise, and is analogous to digital PCR but amendable to quantifying a whole transcriptome. We
demonstrated transcriptome profiling of E. coli with more accurate and reproducible quantification
than conventional RNA-Seq.
2
The central goal of transcriptome profiling is to accurately quantify the abundance of RNA transcripts in a
sample.
While hybridization-based approaches like DNA microarrays can provide only a relative,
analog measure of transcript abundance, sequencing-based approaches such as RNA-Seq have the
advantage of removing hybridization bias among genes (1, 2) and offer the promise of true digital
quantification.
The interpretation of conventional RNA-Seq is complicated by sequence-dependent bias and
amplification noise from reverse transcription, adapter ligation, library amplification by PCR, solid-phase
clonal amplification, and sequencing (3-5).
NanoString technology mitigates these complications by
eliminating enzymatic reactions and hybridizing color-coded probes directly to RNA for single molecule
detection (6), though it requires many specific probes.
Other methods reduce bias in RNA-Seq by
eliminating PCR and directly sequencing single molecules of RNA (7) or sequencing single molecules (8)
or clonal populations (9) of cDNA.
However, library amplification is desirable for sequencing small
samples or single cells (10).
Conventional library amplification is based on PCR, but the exponential amplification afforded
by PCR introduces noise, especially at low copy numbers (11).
Digital PCR was introduced to
circumvent this problem by distributing DNA molecules into many containers, each receiving zero or one
molecules, which are amplified and detected by PCR (12). This technique has been successfully applied
to RNA counting (13). However, it requires specific primers for each gene, which hinders highthroughput measurements.
Here we report a system-wide method for bias and noise reduction in RNA-Seq that allows the
use of PCR to amplify a cDNA library prior to sequencing, providing accurate digital quantification of the
transcriptome.
In our approach, each cDNA molecule is attached to a unique barcode sequence from a
large pool of barcodes prior to amplification (Fig. 1A) (14). Deep sequencing then allows quantification
of the number of cDNA molecules in the original sample by counting the number of unique barcode
sequences associated with a given cDNA sequence. This concept has been applied recently for studying
protein-RNA interactions (15), to improve the sensitivity of DNA mutation detection (16, 17) and
accuracy of DNA copy number measurements for individual genes by threshold detection (18), and to
perform karyotyping and mRNA profiling (19).
However, barcode identification in these studies was
not immune to errors incurred during library preparation, amplification, and sequencing, which can
convert one barcode into another.
Hence, a substantial fraction of reads contained misidentified
barcodes (16-19), which in some cases were discarded using an artificial threshold (17-19). To avoid
this complication, we designed optimized barcodes that can be ligated and amplified with minimal bias
and distinguished from one another despite the accumulation of PCR mutations and sequencing errors.
3
RESULTS
Barcoding Strategy for Digital RNA-Seq. Fig. 1A depicts the general concept of digital counting by
random labeling of all target nucleic acid molecules in a sample with unique barcode sequences. To
achieve unique barcoding of as many target sequences as possible, the set of barcode sequences
introduced to the sample must be 1) much larger than the copy number of the most abundant target
sequence and 2) sampled randomly by the target sequences. If these two criteria are satisfied, then
digital quantification of the target molecules by this method is limited only by sequencing depth and
accuracy. Unlike conventional sequencing-based approaches to nucleic acid quantification, the digital
counting technique is no longer limited by intrinsic amplification noise and bias in downstream sample
preparation and sequencing (Fig. 1A).
Implementation of the scheme in Fig. 1A for digital RNA-Seq requires several critical
considerations. As noted above, if the barcode sequences are random, then a sequencing error at one
position in a barcode will cause that barcode to be misidentified. This error-induced interconversion will
occur even if the barcode sequences are non-random (18), unless the barcodes are carefully designed so
that multiple substitution errors and indels do not obscure their identities (20). Because DNA secondary
structure can reduce amplification efficiency, the barcodes should not have significant sequence overlap
or complementarity with each other, the adapter and primer sequences used in library preparation and
sequencing, or the transcriptome-of-interest. Ideally, the barcode set will not contain sequence motifs
that are known to be problematic for sequencing chemistries such as long homopolymers and regions with
high or low GC-content.
We used a computer program to generate a set of 145 barcode sequences 20 base-pairs in length
(Table S1) that satisfies the above criteria (Materials and Methods and SI Materials and Methods). The
barcode sequences can sustain up to four substitution errors and remain unambiguously identifiable.
In
addition, a barcode that incurs up to nine substitution errors or the combination of one indel and five
substitution errors will not take on the sequence of another barcode.
Instead of using a single barcode sequence to identify each target molecule in our sample (15-19),
we attached a barcode sequence to both ends of each target molecule (Fig. 1B, SI Materials and Methods).
If both ends of a target sequence sample all of the barcodes randomly, the target sequence will have
access to 145x145 = 21,025 unique labels. The two barcode sequences along with the target molecule
sequence were then read out by paired-end sequencing (Fig. 1B). This paired-end strategy dramatically
reduces the number of barcodes that must be designed and synthesized, is compatible with conventional
paired-end library protocols, and provides long-range sequence information which improves mapping
accuracy (21, 22). In addition, attaching barcodes to both ends increases the overall randomness of
barcode sampling because the two ends of a target molecule are unlikely to have a similar degree of bias.
4
We tested and characterized this method on a set of quantified DNA spike-in sequences and a cDNA
library derived from the transcriptome of E. coli.
Quantification of Spike-In Sequences and Barcode Sampling Bias. To calibrate our digital RNA-Seq
system, we measured the concentrations of five synthetic DNA spike-in sequences using the Fluidigm
digital PCR platform and used them as internal standards. The spike-in samples were barcoded, added
to the barcoded E. coli cDNA library, and quantified using the sequencing-based digital counting strategy
described above.
Fig. 2A shows that the number of digital counts (i.e. unique barcodes) observed in
deep sequencing is well-correlated with the digital PCR calibration of the spike-in sequences.
To evaluate the difference between using random barcode sequences and our optimized barcode
sequences, we conducted two experiments.
In one experiment, we labeled the spike-in molecules with
random barcode sequences (SI Materials and Methods), and in the second experiment, we used our
optimized, pre-determined barcode set. We constructed the histograms of the number of reads for all
barcodes observed from the most abundant spike-in sequence (Fig. 2B).
When using random barcodes
(red histogram in Fig. 2B and SI Materials and Methods), the left-most bin exhibits a large peak because a
substantial fraction of barcodes are infrequently read due to sequencing errors. This causes barcodes to
interconvert, generating quantification artifacts which were also evident in previous reports (16-19). In
stark contrast, the left-most bin when using optimized barcodes (green histogram in Fig. 2B) has no such
peak because our optimized barcode sequences avoid misidentification due to sequencing errors. The
effect of sequencing error on both random and optimized barcode counting is clearly shown by simulation
(Fig. S1, SI Materials and Methods).
We note that the green histogram in Fig. 2B is the distribution of the number of reads for the
5,311 uniquely barcoded molecules from a particular spike-in (SI Materials and Methods). Assuming
each barcoded spike-in molecule is identical, the green histogram in Fig. 2B is essentially the probability
distribution of the number of reads for a single molecule, which spans three orders-of-magnitude. This
broad distribution arises primarily from intrinsic PCR amplification noise (11) in sample preparation.
Given this broad single molecule distribution, for low copy molecules in the original sample, counting the
total number of reads (conventional RNA-Seq) would be catastrophic. On the other hand, this problem
can be circumvented if one counts the number of different barcodes (integrated area of the histogram)
using our digital RNA-Seq approach, yielding accurate quantification with single copy resolution. The
two counting schemes give same results only when the copy number in the original sample is high,
assuming there is no sequence-dependent bias.
Random sampling of the barcode sequences by each target sequence is essential for accurate
digital counting.
Fig. 2C shows that the distribution of observed molecule counts is in excellent
5
agreement with Poisson statistics. Therefore the five spike-in sequences sample the 21,025 barcode
pairs without bias.
Digital Quantification of the E. coli Transcriptome. We obtained 26-32 million reads from our
barcoded cDNA libraries that uniquely mapped to the E. coli genome (Materials and Methods and Table
S2) in two replicate experiments.
Fig. 3A shows the number of conventional and digital counts (unique
barcodes) as a function of nucleotide position for the fumA transcription unit (TU). Not surprisingly, the
read density is considerably less uniform across the TU than the number of digital counts, presumably due
to intrinsic noise and bias in fragment amplification.
It is crucial for transcripts across the E. coli transcriptome to sample all barcodes evenly.
3B shows this distribution, which is close to Poisson but is somewhat overdispersed.
Fig.
Such biased
sampling reduces the effective number of barcode sequences Neff available. However, in our E. coli
transcriptome sample, the copy number of the most abundant cDNA ranges from 10-40 copies for both
counting methods.
Based on Poisson statistics, even for the most abundant cDNA fragments in our
sample, the required Neff is ~100-400 for 95% unique labeling of all molecules (18).
Because there are
21,025 barcode pairs available, on average the degree of randomness observed in Fig. 3B is sufficient.
The conventional method counts the number of amplicons, a quantity that is subject to bias and
intrinsic amplification noise (11), rather than the number of molecules in the original sample.
Conversely, in our digital counting scheme, unique barcode sequences distinguish each molecule in the
sample, and so the effects of intrinsic noise are minimized.
Fig. 3C shows how drastically different
digital counting can be from conventional counting at low copy numbers, implying that digital counting
of unique barcodes is advantageous, particularly for quantifying low copy fragments.
We note that the
correlation is stronger for high copy fragments and the same phenomenon is also observed for whole TUs
and genes (Fig. S2).
To demonstrate the superior accuracy of digital counting, we examined the uniformity of our
abundance measurements within individual transcripts.
Because individual TUs were, by-and-large,
intact RNA molecules following RNA synthesis, the cDNA fragments that map to one region of a given
TU should have the same abundance as fragments that map to a different region of the same TU.
We
histogrammed the ratio between the variation in conventional counting C and variation in digital
counting D for TUs in different abundance ranges (Fig. 3D). A variation ratio of C/D = 1 indicates
that both conventional and digital counting give similarly uniform abundances along the length of a TU.
For a TU where C/D exceeds one, conventional counting measures abundance less consistently along the
TU than digital counting.
The mean values of C/D in the two replicates are 1.4 (s=1.5, where s is
sample standard deviation) and 1.2 (s=0.5) for the complete set of analyzed TUs, indicating that
6
conventional counting is less consistent than digital counting across an average TU. Furthermore, the
mean value of C/D increases with decreasing copy number and its distribution becomes broader (Fig.
3D). For TUs in the lowest abundance regime, the mean values of C/D are 1.9 (s=2.4) and 1.3 (s=0.9)
for the two replicates.
We conclude that, on average, digital counting outperforms conventional
counting in terms of accuracy, and its performance advantage is most pronounced for low abundance TUs.
While Fig. 3 demonstrates that digital counting is less noisy and more accurate than conventional
counting, Fig. 4 shows that digital counting is also more reproducible.
We demonstrate this on the level
of a single TU in Fig. 4A, which shows the ratio of counts between the two replicates for both
conventional and digital counting along the fumA transcript. This ratio is consistently close to one for
digital counting, but fluctuates over three orders-of-magnitude for conventional counting.
We analyzed
the global reproducibility of the whole transcriptome for quantification of TUs and genes for both
conventional and digital counting in Fig. 4B and Fig. 4C, respectively.
In both cases, the correlation
between replicates is noticeably better for digital counting than conventional counting, particularly for
low copy transcripts.
Discussion
Unlike previously reported methods of eliminating bias and noise from RNA-Seq (7-9), our strategy
allows amplification by PCR and uses standard commercial protocols for sample preparation.
the implementation described above also leaves considerable room for improvement.
However,
For example, one
could ligate barcoded adapters directly to RNA (23, 24), reducing the bias that occurs during reverse
transcription.
Alternatively, a recently described protocol for processing mature mRNA from single
mammalian cells could be modified to include barcoded primers for reverse transcription and second
strand synthesis prior to amplification (10), obviating the need for ligation.
One disadvantage of our technique is that it requires higher sequencing coverage than
conventional RNA-Seq. This is because both the transcriptome and the barcode set must be evenly
sampled for accurate counting.
However, the cost-per-base of deep sequencing continues to decrease
rapidly. In our experiment, the mean number of reads per fragment was ~400.
However, the spike-in
sequencing reads can be randomly downsampled 10-fold (SI Materials and Methods) without perturbing
the correlation between abundance measured by digital PCR and digital barcode counting (Fig. S3).
This implies that significantly lower coverage will suffice in many cases.
For applications where many cycles of PCR are required for sensitive detection, bias and noise
reduction are crucial for accurate quantification.
Although we demonstrated our technique on the E. coli
transcriptome, we note that the maximum copy number for polyadenylated mRNA in a single mouse
blastomere was found to be ~2,400 (10). With 155 optimized barcode sequences (10 more than were
7
used in this study), one could uniquely label nearly every identical molecule in this system (with 95%
unique labeling for even the most abundant transcript).
Hence, we expect this technique will be readily
applicable to eukaryotic systems without substantial modification.
In addition, we analyze the
performance of digital and conventional counting in a simulation of differential expression analysis, a key
application of RNA-Seq (Fig. S4). Our simulation, which accounts for experimentally measured copy
number, barcode sampling bias, and amplification noise distributions, shows that digital counting of
unique barcodes outperforms conventional counting for differential expression analysis (SI Materials and
Methods).
Although it is always more difficult to reject the null hypothesis for low abundance
transcripts, we expect our digital counting scheme to be nonetheless more accurate than conventional
counting for differential expression analysis at low copy numbers.
In addition to single cell applications, we expect this technique to be particularly useful for
nascent transcript sequencing by run-on (25) or RNA polymerase capture (26), ribosome profiling (27),
and profiling of miRNA and other regulatory RNAs which typically exist at low copy numbers.
Significant recent progress has been made in minimizing bias induced by sample barcodes for
multiplexed miRNA-Seq (28), and we expect that this technique could be applied to the introduction of
barcodes for digital counting in any RNA-Seq experiment.
In addition, one could use our approach to
improve DNA sequencing experiments such as chromatin immunoprecipitation sequencing (ChIP-Seq)
(29) which is procedurally related to RNA-Seq and exposed to similar sources of bias and noise (30).
RNA-Seq holds substantial promise for basic research in biomedicine and may ultimately impact
clinical diagnostics (21, 31, 32).
However, challenges ranging from bias in sample preparation to
limited sensitivity and remain significant.
Digital RNA-Seq, along with continued improvements to
sequencing technology, will lead to new applications and allow RNA-Seq to reach its full potential.
Materials and Methods
Generation and Optimization of Barcodes. We generated 2,358 random 20-base barcode candidates
using a computer such that even if a barcode accumulated nine mutations, it would not take the sequence
of any other generated barcode sequences (unlike the random barcode case SI Material and Methods,
(Dataset S3)).
Barcode candidates containing homopolymers longer than four bases or GC-content less
than 40% or greater than 60% were discarded.
Barcode candidates were also discarded if each exceeded
a certain degree of complementarity or sequence identity (total matches and maximum consecutive
matches) with (1) the Illumina paired-end sequencing primers (33), (2) the Illumina PCR primers PE 1.0
and 2.0, (3) the 3’ end of the Illumina PCR primers PE 1.0 and 2.0, (4) the whole E. coli genome [K-12
MG1655 strain (U00096.2)], and (5) all other generated barcode candidates (SI Materials and Methods).
8
Any barcode candidate for which an indel mutation would place it within five point mutations of another
barcode candidate was also discarded. The final population consisted of 150 barcodes, of which 145 were
randomly chosen and used (Table S1).
E. coli RNA Preparation and cDNA Generation. The cDNA library of E. coli [K-12 MG1655 strain
(U00096.2)] was generated by a standard method (SI Materials and Methods).
Sample-Adapter Ligation, Sequencing Sample Preparation, and Sequencing. The cDNA library was
ligated to the barcode adapter mixture, and the sequencing sample was prepared by the standard Illumina
protocol with some modifications along with an internal standard (SI Materials and Methods, Dataset S4).
E. coli Transcriptome Analysis. From the raw sequencing data, we isolated reads which contained
barcode sequences that corresponded to our original list of 145 barcodes in both forward and reverse
reads for each sequencing cluster that had at most one mismatch. We then aligned the first 28 bases (26
bases for the second sequencing run) of the targeted sequence of both the forward and reverse reads of
each cluster to the E. coli genome and kept the sequences that uniquely align fewer than three mismatches
and where the two reads did not map to the same sense or antisense strand of the genome.
The
remaining sequences were mapped to transcription units (34) and sorted by starting and ending position as
well as forward and reverse barcodes (unique tag). Mapped sequence fragments with a length of at least
1,000 bases were discarded. All sequences within the same transcription unit that had the same unique
tag were analyzed further. We determined that more than one sequence with the same unique tag were
identical if the distance between their center positions was less than four base-pairs and if the difference
in length was less than 9 base-pairs (Fig. S5 and Fig. S6). Thus, the read counts for sequences deemed
identical were summed and the sequence with more read counts was deemed as the actual correct
sequence. Then for each unique sequence, we counted the number of unique barcode tags that appeared
to determine the copy number of each sequence.
The genome wide expression profile by digital
counting and conventional counting are visualized by Integrated Genome Browser (SI Materials and
Methods).
ACKNOWLEDGEMENTS. This work was supported by the United States National Institutes of Health
National Human Genome Research Institute Grant (HG005097-01) to X.S.X. and the United States
National Institutes of Health National Human Genome Research Institute Recovery Act Grand
Opportunities Grant (1RC2HG005613-01) to X.S.X. K.S. was supported by a Postdoctoral Fellowship
for Research Abroad from the Japanese Society for the Promotion of Science and a fellowship from The
Uehara Memorial Foundation. Illumina sequencing was performed at the Harvard FAS Center for
Systems Biology with the help of Christian Daly and at the Tufts University School of Medicine
Genomics Core Facility with the help of Kip Bodi and James Schiemer. Digital PCR was performed by
9
the Fluidigm Genetic Analysis Facility at the Molecular Genetics Core Facility of the Children’s Hospital
Boston Intellectual and Developmental Disabilities Research Center (IDDRC) with the help of Hal
Schneider and Ta-Wei Lin.
Base-calling analysis was performed at the Harvard FAS Research
Computing Group by Jiangwen Zhang.
10
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Figure Legends
Fig. 1. Our scheme of digital RNA-Seq. (A) General principle of digital RNA-Seq.
Assume the
original sample contains two cDNA sequences, one with three copies and another with two copies. An
overwhelming number of unique barcode sequences are added to the sample in excess, and five are
randomly ligated to the cDNA molecules.
Ideally, each cDNA molecule in the sample receives a unique
barcode sequence. After removing the excess barcodes, the barcoded cDNA molecules are amplified by
PCR.
Because of intrinsic noise and sequence-dependent bias, the barcoded cDNA molecules are
amplified unevenly.
Consequently, after the amplicons are sequenced, it appears that there are three
copies of cDNA1 for every four copies of cDNA2 based on the relative number of reads for each
sequence. However, the ratio in the original sample was 3:2, which is accurately reflected in the relative
number of unique barcodes associated with each cDNA sequence. (B) In our implementation of (A), we
found it advantageous to randomly ligate both ends of each phosphorylated cDNA fragment to a barcoded
phosphorylated Illumina Y-shaped adapter.
Note that the single T and A overhangs present on the
barcodes and cDNA, respectively, are to enhance ligation efficiency.
After this step, the sample is
amplified by PCR and prepared for sequencing using the standard Illumina library protocol. For each
amplicon, both barcode sequences and both strands of the cDNA sequence are read using paired-end deep
sequencing.
Fig. 2. Spike-in sequence quantification. (A) Correlation between the number of spike-in molecules for
five different spike-in sequences as measured by digital PCR and digital counting of unique barcodes. The
theoretical curve, which saturates due to the finite number of barcode pairs (21,025), is calculated based
on the Poisson distribution (18). (B) Histograms of the number of reads corresponding to each observed
barcode attached to the most abundant spike-in sequence for two experiments. The red histogram
corresponds to a spike-in sequence labeled with random barcode sequences, and the green histogram
corresponds to a spike-in sequence labeled with our optimized barcodes.
Note the leftmost bin in the red
histogram is >10 times larger than that of the green histogram and contains a large number of unique
barcodes with a low number of reads. This is caused by various sequencing and PCR amplification
errors which generate new artifactual unique barcodes not present in the original sample and result in a
large number of falsely identified unique barcodes (SI Materials and Methods). The inset shows the red
histogram in greater detail.
(C) Histogram of the number of times a barcode pair was observed with all
five spike-in sequences (i.e. the number of spike-in molecules attached to a given barcode pair).
Because the spike-in sequences sample the barcode pairs randomly with very little bias, the histogram
follows a Poisson distribution.
13
Fig. 3. Digital quantification of the E. coli transcriptome. (A) Conventional and digital counting results
for the fumA transcription unit (TU) as a function of genome position. The conventional counts were
calculated by using a conventional calibration curve which allows regression of the number of reads
against the number of input molecules for all spike-in molecules (Fig. 2A). The digital counts were
obtained by counting the number of unique barcodes associated with each fragment.
the ratios of these two numbers for each base.
The red dots are
(B) Histograms of the number of times a barcode pair was
observed with the E. coli cDNA sequences (i.e. the number of cDNA molecules attached to a given
barcode pair) in the two replicates. Barcode sampling is more biased on average for E. coli cDNA
fragments, but is still in reasonably good agreement with Poisson statistics.
(C) Correlation between the
number of reads (conventional counting) and the number of molecules obtained from digital counting of
unique barcodes for every mapped fragment in the two replicates.
For low copy molecules, the
conventional counts are distributed over three orders-of-magnitude. This is because the conventional
method counts amplicons which are subject to intrinsic noise (11), rather than directly counting molecules
in the original samples like the digital counting method. We note that higher copy fragments are less
affected by intrinsic noise (11) as the number of molecules sequenced is greater; this effectively allows
averaging over the read counts of many molecules in conventional RNA-Seq, decreasing the variance of
counting in the process. (D) Uniformity of conventional vs. digital counting along the length of each TU
as a function of TU abundance across the whole E. coli transcriptome for both replicates. We calculated
the variation D = sD/D (where D and sD are the mean and sample standard deviation of the digital
counts among 99-base bins in a TU, respectively) associated with digital counting and the variation C
=sC/C associated with conventional counting within each TU for which at least three bins contained on
average at least one read.
We then created the histogram of the ratio between conventional and digital
counting variation (C/D) for TUs in different abundance ranges for each replicate. TU abundance is
the sum of all digital counts for each fragment in the TU.
Fig. 4. Reproducibility of digital and conventional quantification of the E. coli transcriptome.
(A) Ratio
of counts between two replicate sequencing runs normalized by total uniquely mapped reads for digital
counting plotted along with the ratio of counts between the two replicates for conventional counting of the
fumA TU. As expected, the ratio fluctuates over a broader range for conventional counting than digital
counting along the length of the TU.
conventional counting of TUs.
(B)
Correlation between replicate sequencing runs for digital and
DPKM represents the uniquely mapped digital counts per kilobase per
million total uniquely mapped molecules. RPKM represents the uniquely mapped reads per kilobase per
million total uniquely mapped reads. (C)
Correlation between replicate sequencing runs for digital and
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conventional counting of genes.
Taken together, (B) and (C) demonstrate that digital counting is
globally more reproducible than conventional counting.
FOOTNOTES
*
To whom correspondence should be addressed. E-mail: xie@chemistry.harvard.edu
Author contributions: K.S., T.Z.J., P.A.S., and X.S.X designed research; K.S. and T.Z.J. performed
research; K.S., T.Z.J., and P.A.S. analyzed the data; K.S., T.Z.J., P.A.S., and X.S.X. wrote the manuscript.
All
supplementary
tables
(S1-S7)
may
be
found
at
the
following
location:
http://bernstein.harvard.edu/digitalRNA-Seq/
The authors declare that Harvard University has filed a provisional patent application based on this work.
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